This letter presents a novel radar based, single-frame, multi-class detection method for moving road users ( pedestrian, cyclist, car ), which utilizes low-level radar cube data. The method provides class information both on the radar target- and object-level. Radar targets are classified individually after extending the target features with a cropped block of the 3D radar cube around their positions, thereby capturing the motion of moving parts in the local velocity distribution. A Convolutional Neural Network (CNN) is proposed for this classification step. Afterwards, object proposals are generated with a clustering step, which not only considers the radar targets’ positions and velocities, but their calculated class scores as well. In experiments on a real-life dataset we demonstrate that our method outperforms the state-of-the-art methods both target- and object-wise by reaching an average of 0.70 (baseline: 0.68) target-wise and 0.56 (baseline: 0.48) object-wise F1 score. Furthermore, we examine the importance of the used features in an ablation study.